few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Understand and evaluate random processes underlying statistical experiments.

Investigate patterns of association in bivariate data.

Interpret linear models.

Calculate expected values and use them to solve problems.

Develop understanding of statistical variability.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Summarize and describe distributions.

Investigate chance processes and develop, use, and evaluate probability models.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Summarize, represent, and interpret data on a single count or measurement variable.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use probability to evaluate outcomes of decisions.

Understand independence and conditional probability and use them to interpret data.

Use random sampling to draw inferences about a population.

Draw informal comparative inferences about two populations.
problem_activity: Warm-up
The mathematical purpose of this activity is for students to match bivariate data with its context. Students should think about whether they might expect a strong correlation or not as well as whether the relationship has a positive or negative correlation. Monitor for students who discuss linear relationships or variability in the data.
Launch
Arrange students in groups of two to four. Provide access to the scatter plots and contexts for the warm-up.
Student Facing
Match the variables to the scatter plot you think they best fit. Be prepared to explain your reasoning.
|    | \(x\)                  variable | \(y\)                  variable |
|----|---------------------------------|---------------------------------|
| 1. |                                 |                                 |
| 2. |                                 |                                 |
| 3. |                                 |                                 |
| 4. |                                 |                                 |
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may struggle with matching the pairs of variables with a scatter plot. Encourage students to think about how related the variables are and how the
\(y\)
variable might change as the
\(x\)
variable increases.
Activity Synthesis
The goal of this discussion is for students to discuss how the characteristics of the scatter plots allowed them to determine the context. For each context, select groups to share their match and reasoning. Select groups who used linear model and variability in their small group discussions.
Here are some questions for discussion.
“How did the concept of linear relationships help you to make a match?” (For the height in inches and the height in feet, I knew that the data would be very linear. I chose scatter plot A because it was the only one that appeared linear. I did wonder why scatter plot A was not perfectly linear. Maybe it had to do with rounding or measurement error.)
“How did you use the concept of linearity to help you to make a match?” (First, I expected the temperature and cereal context relationship to be totally random rather than linear at all, so that fit with scatter plot C. Second, I knew that problem 3 matched with scatter plot A, because I knew it should be almost perfectly linear. For a given height in feet, there is only one height in inches.)
“Which matches were the most difficult? What helped you figure them out?” (It was hardest to find the matches for scatter plots B and D because they were pretty scattered. I noticed that the data in scatter plot D displayed a negative relationship, so I looked for a context that would have a negative relationship. It makes sense that customer satisfaction decreases as wait time increases.)


correct_option_index: 5